A Galerkin Boundary Element Method for a High Frequency Scattering Problem

on Γ := {(x1, 0) : x1 ∈ R}, where k > 0 (the wavenumber) is some arbitrary positive constant. This boundary value problem can arise when modelling the acoustic scattering of an incident wave by a planar surface with spatially varying acoustical properties [1]. The total acoustic field u ∈ C(U)∩C(U) satisfies (1)– (2) where the wavenumber k = 2πμ/c, with μ being the frequency of the incident wave, c the speed of sound in U , and f ≡ 0. For simplicity of exposition, here we restrict our attention to the case of plane wave incidence, so that the incident field u is given by u(x) = e, d = (d1, d2) = (sin θ,− cos θ), (3)